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The $ρ$ Meson Light-Cone Distribution Amplitudes of Leading Twist Revisited

P. Ball, V. M. Braun

TL;DR

This work re-evaluates the leading-twist quark-antiquark light-cone distribution amplitudes of the $\rho$ meson, deriving Wandzura-Wilczek type relations and updating the conformal expansion coefficients $a_n(\mu)$ using next-to-leading order QCD sum rules. It shows that the longitudinal and transverse DAs, $\phi_\parallel$ and $\phi_\perp$, have similar shapes, contradicting earlier analyses, and provides updated values for the tensor coupling $f_\rho^{\perp}$ and the Gegenbauer moments $a_2^{\parallel}$ and $a_2^{\perp}$ with radiative corrections. The results rely on a careful treatment of parity contamination in sum rules and establish WW-type relations for transverse spin distributions in a longitudinally polarized $\rho$, mirroring the nucleon $g_1$–$g_2$ framework. The improved nonperturbative inputs are expected to impact predictions for hard exclusive processes, including vector-meson production and exclusive $B$ decays, where transverse polarization effects are relevant.

Abstract

We give a complete re-analysis of the leading twist quark-antiquark light-cone distribution amplitudes of longitudinal and transverse $ρ$ mesons. We derive Wandzura-Wilczek type relations between different distributions and update the coefficients in their conformal expansion using QCD sum rules including next-to-leading order radiative corrections. We find that the distribution amplitudes of quarks inside longitudinally and transversely polarized $ρ$ mesons have a similar shape, which is in contradiction to previous analyses.

The $ρ$ Meson Light-Cone Distribution Amplitudes of Leading Twist Revisited

TL;DR

This work re-evaluates the leading-twist quark-antiquark light-cone distribution amplitudes of the meson, deriving Wandzura-Wilczek type relations and updating the conformal expansion coefficients using next-to-leading order QCD sum rules. It shows that the longitudinal and transverse DAs, and , have similar shapes, contradicting earlier analyses, and provides updated values for the tensor coupling and the Gegenbauer moments and with radiative corrections. The results rely on a careful treatment of parity contamination in sum rules and establish WW-type relations for transverse spin distributions in a longitudinally polarized , mirroring the nucleon – framework. The improved nonperturbative inputs are expected to impact predictions for hard exclusive processes, including vector-meson production and exclusive decays, where transverse polarization effects are relevant.

Abstract

We give a complete re-analysis of the leading twist quark-antiquark light-cone distribution amplitudes of longitudinal and transverse mesons. We derive Wandzura-Wilczek type relations between different distributions and update the coefficients in their conformal expansion using QCD sum rules including next-to-leading order radiative corrections. We find that the distribution amplitudes of quarks inside longitudinally and transversely polarized mesons have a similar shape, which is in contradiction to previous analyses.

Paper Structure

This paper contains 10 sections, 62 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The $\rho$ Meson Distribution Amplitudes
  3. Definitions
  4. Conformal Expansion and Renormalization
  5. Non-Perturbative Input
  6. Transversely Polarized $\rho$ Mesons
  7. The Tensor Coupling
  8. Deviations from the Asymptotic Form
  9. Longitudinally Polarized $\rho$ Mesons
  10. Summary and Conclusions

Figures (5)

  • Figure 1: (a) $f_\rho^\perp(1\,{\rm GeV})$ from Eq. (\ref{['eq:SRft2']}) as function of the Borel parameter $M^2$ for different values of the continuum threshold $s_0$. (b) The same for $f_{b_1}^\perp(1\,{\rm GeV})$ from Eq. (\ref{['eq:SRft3']}).
  • Figure 3: $f_\rho^\perp(1\,{\rm GeV})$ from Eq. (\ref{['eq:nondiagonal']}) as function of the Borel parameter $M^2$ for $s_0=1.5\,{\rm GeV}^2$.
  • Figure 4: $a_2^\perp(1\,{\rm GeV})$ from Eq. (\ref{['eq:SRa2t']}) as function of the Borel parameter $M^2$ for $s_0 = 1\,$GeV$^2$.
  • Figure 5: $a_2^\parallel(1\,{\rm GeV})$ from Eq. (\ref{['eq:SRa2l']}) as function of the Borel parameter $M^2$ for $s_0=1.5\,{\rm GeV}^2$.
  • Figure 6: Final results for the wave functions $\phi_\parallel$ (a) and $\phi_\perp$ (b) at $\mu = 1\,$GeV (solid lines). Long dashes: asymptotic wave functions, short dashes: $\phi_\perp$ according to CZ CZreport.